Bifurcations in a class of complex differential equations

In this paper we introduce a class of nonlinear complex ordinary differential equations that arises in the removal of channel distortion in digital telecommunication signals. Techniques from dynamical systems theory show that Hopf bifurcations are possible in the simplest of these systems. Numerical integrations, however, show that such bifurcations are degenerate. When attempts are made to follow the periodic orbits, both the period of oscillation and the principal bifurcation parameter remain fixed at their values at bifurcation. The periodic orbits exist as a family at discrete parameter values, i.e. we have a nonlinear centre. A stability régime diagram is presented. © 1992, Cambridge University Press. All rights reserved.